Year
2024Credit points
10Campus offering
Prerequisites
NilUnit rationale, description and aim
Mathematics is a discipline with its own values and aesthetics, derived from the abstractedness and orderliness of mathematics. Typically, school mathematics is focused on developing an understanding of mathematical content topics, informed by curriculum and syllabus documents. Students have limited opportunities to develop an aesthetic appreciation of mathematics as a discipline, or different ways of engaging with and thinking about mathematics.
This unit offers a historical overview of the development of number and how this varies in different societies and cultures. Throughout the unit, pre-service teachers will engage in the process of working mathematically, including conjecturing, specialising, generalising, justifying, mathematising, proving together with argumentation problem posing, problem solving, investigation and mathematical modelling. These processes will be contextualised within historical and real-world situations and support the rationale of the Australian Curriculum Mathematics (v.9) in developing students’ appreciation of the power of mathematical reasoning as they develop mastery of the content in mathematics.
The aim of this unit is to develop pre-service teachers’ understanding of the discipline of mathematics along with developing their mathematical content knowledge.
Learning outcomes
To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.
Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.
Explore the graduate capabilities.
| Learning Outcome Number | Learning Outcome Description | Relevant Graduate Capabilities |
|---|---|---|
| LO1 | Explain the historical development of number and the effect this development has had on different societies and cultures | GC1, GC2, GC5, GC7, GC9, GC11 |
| LO2 | Demonstrate an understanding of the real number system, including rational numbers and irrational numbers, and solve problems involving real numbers using digital tools and other resources | GC1, GC2, GC8, GC10 |
| LO3 | Engage in working mathematical processes including conjecturing, generalising, modelling and computational thinking | GC1, GC2, GC10, GC11 |
| LO4 | Use working mathematically processes to solve a variety of problems involving number and algebraic applications | GC1, GC2, GC8 |
Australian Professional Standards for Teachers - Graduate Level
On successful completion of this unit, pre-service teachers should have developed the following industry specific knowledge based on the Australian Professional Standards for Teachers - Graduate Level standards:
| Industry Standard | Relating to | Relevant Learning Outcome |
|---|---|---|
| APST(GA)2.1 | Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area. | LO1, LO2, LO3, LO4 |
Content
The use of technology will be utlilised throughout all topics allowing students to focus on understanding, rather than the mechanics of each particular topic.
The importance of numbers
- What is the purpose of numbers? Why have different cultures developed numbers? How do number systems and representations vary across cultures?
- Number systems from other cultures (e.g., Babylonian, Aboriginal and Torres Strait Islanders)
- Types of numbers (natural, integer, rational)
- Working with numbers in the real world (place value of numbers, computational thinking, algorithms, critical numeracy, including data interpretation)
Number systems and number representations
- The extension of place value to very large and very small numbers
- Different place value bases; different ways of representing numbers and conversion between them
Working with whole numbers
- Choosing appropriate representations; operating with whole numbers and integers working with whole numbers and integers.
- Types of whole numbers: Primes, greatest common divisor, Euclidean algorithm
- Solve problems involving real numbers using digital tools
- Solving equations needing whole numbers; linear inequalities and linear equations; simplifying expressions and solving equations algebraically; distributive property
Learning and teaching strategy and rationale
Teaching and learning organisation can take several forms. This could include intensive weekend classes supported by web-based tools, Intensive one week winter or summer schools supported by web-based tools or weekly face-to-face classes during semester.
Pre-service teachers may be expected to participate in online discussion and sharing via eLearning. Class resources will be available via eLearning as will access to relevant web links.
This is a 10-credit point unit and has been designed to ensure that the time needed to complete the required volume of learning to the requisite standard is approximately 150 hours in total across the semester. To achieve a passing standard in this unit, students will find it helpful to engage in the full range of learning activities and assessments utilised in this unit, as described in the learning and teaching strategy and the assessment strategy. The learning and teaching and assessment strategies include a range of approaches to support your learning such as reading, reflection, discussion, webinars, podcasts, video etc.
Duration
This is a 10-credit point unit and has been designed to ensure that the time needed to complete the required volume of learning to the requisite standard is approximately 150 hours in total across the semester.
Assessment strategy and rationale
The assessment tasks for this unit have been designed to contribute to high quality student learning by both helping students learn (assessment for learning), and by measuring explicit evidence of their learning (assessment of learning). Assessments have been developed to meet the unit learning outcomes and develop graduate attributes consistent with University assessment requirements. The assessment tasks provide multiple opportunities (presentation, problem solving and examination) in different ways (visual, verbal and written) for students to demonstrate:
- Knowledge of content
- Application of mathematics in real world contexts
- Understanding of historical, aesthetic and cultural mathematics
- Development, use and communication of appropriate mathematical language
Minimum Achievement Standards
The assessment tasks for this unit are designed to demonstrate achievement of each learning outcome.
In order to pass this unit, students are required to complete all required assessment tasks as per the Assessment Policy and gain an overall pass mark.
Overview of assessments
| Brief Description of Kind and Purpose of Assessment Tasks | Weighting | Learning Outcomes | Graduate Capabilities | Standards |
|---|---|---|---|---|
Assessment Task 1: Early Skills Assessment Early skills test or assignment, designed to allow students to demonstrate what they have learned. | 20%
| LO1, LO2 | GC1, GC2, GC5, GC7, GC8, GC9, GC10, GC11 | APST(GA)2.1 |
Assessment Task 2: Learning from Others Investigate how numbers and number skills in mathematics were developed and used within an Indigenous culture to solve a particular problem or problems. Discuss whether the use of this aspect of mathematics has changed over time within the chosen culture. Presentation of findings in a 1500-word summary. | 40%
| LO1, LO2, LO3 | GC1, GC2, GC5, GC7, GC8, GC9, GC10, GC11 | APST(GA)2.1 |
Assessment Task 3: Final Examination: Written test covering the skills and concepts from the unit. | 40% | LO1, LO2, LO3, LO4 | GC1, GC2, GC5, GC7, GC8, GC9, GC10, GC11 | APST(GA)2.1 |
Representative texts and references
Australian Curriculum https://www.australiancurriculum.edu.au/
Australian Curriculum, Assessment and Reporting Authority (ACARA) www.acara.edu.au
McLeod, G. et al (2019). Introduction to mathematical thinking. Custom Edition. Pearson.
Australian Curriculum Mathematics v.9. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
Relevant state and territory Mathematics curriculum documents
Recommended references
Bellos, A. (2015). Alex through the looking glass: How life reflects numbers, and numbers reflect life. Bloomsbury.
Clapham, C., & Nicholson, J. (2014). The concise Oxford dictionary of mathematics (5th ed.). Oxford University Press.
Du Sautoy, M. (2011). The number mysteries: A mathematical odyssey through everyday life (1st Palgrave Macmillan ed.). Palgrave Macmillan.
Goos, M., Vale, C., Stillman, G., Makar, K. M., Herbert, S., & Geiger, V. (2017). Teaching secondary school mathematics: research and practice for the 21st century (2nd ed). Allen & Unwin.
Joseph, G. G. (2011). The crest of the peacock: Non-European roots of mathematics (3rd ed.). Princeton University Press.
Katz, V. (2009). A history of mathematics (3rd rev. ed.). Pearson Education.
Matthews, C., Cooper, T., & Baturo, A. (2007). Creating your own symbols: Beginning algebraic thinking within Indigenous students. In Woo, J. H., Lew, H. C., Park, K. S. & D.Y. Seo (Eds.). Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 249-256. Seoul: PME.
Wells, D. G. (1987). The Penguin dictionary of curious and interesting numbers. Penguin.